Zahari Zlatev's Books

Richardson Extrapolation

Practical Aspects and Applications

By: Zahari Zlatev,Ivan Dimov,István Faragó,Ágnes Havasi

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Richardson Extrapolation

Practical Aspects and Applications

By: Zahari Zlatev,Ivan Dimov,István Faragó,Ágnes Havasi

Scientists and engineers are mainly using Richardson extrapolation as a computational tool for increasing the accuracy of various numerical algorithms for the treatment of systems of ordinary and partial differential equations and for improving the computational efficiency of the solution process by the automatic variation of the time-stepsizes. A third issue, the stability of the computations, is very often the most important one and, therefore, it is the major topic studied in all chapters of this book. Clear explanations and many examples make this text an easy-to-follow handbook for applied mathematicians, physicists and engineers working with scientific models based on differential equations. Contents The basic properties of Richardson extrapolation Richardson extrapolation for explicit Runge-Kutta methods Linear multistep and predictor-corrector methods Richardson extrapolation for some implicit methods Richardson extrapolation for splitting techniques Richardson extrapolation for advection problems Richardson extrapolation for some other problems General conclusions

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Page Count

310

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110533006

ISBN 13

9783110533002

Computer Treatment of Large Air Pollution Models

By: Zahari Zlatev

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Computer Treatment of Large Air Pollution Models

By: Zahari Zlatev

Models are often the only way of interpreting measurements to in vestigate long-range transport, and this is the reason for the emphasis on them in many research programs". B. E. A. Fisher: "A review of the processes and models of long-range transport of air pollutants", Atmospheric Environment, 17(1983), p. 1865. Mathematical models are (potentially, at least) powerful means in the efforts to study transboundary transport of air pollutants, source-receptor relationships and efficient ways of reducing the air pollution to acceptable levels. A mathematical model is a complicated matter, the development of which is based on the use of (i) various mechanisms describing mathematically the physical and chemical properties of the studied phenomena, (ii) different mathematical tools (first and foremost, partial differenti al equations), (iii) various numerical methods, (iv) computers (especially, high-speed computers), (v) statistical approaches, (vi) fast and efficient visualization and animation techniques, (vii) fast methods for manipulation with huge sets of data (input data, intermediate data and output data).

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367

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401103119

ISBN 13

9789401103114

Computational and Numerical Challenges in Environmental Modelling

By: Zahari Zlatev,Ivan Dimov

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Computational and Numerical Challenges in Environmental Modelling

By: Zahari Zlatev,Ivan Dimov

Many large mathematical models, not only models arising and used in environmental studies, are described by systems of partial differential equations. The discretization of the spatial derivatives in such models leads to the solution of very large systems of ordinary differential equations. These systems contain many millions of equations and have to be handled over large time intervals by applying many time-steps (up to several hundred thousand time-steps). Furthermore, many scenarios are as a rule to be run. This explains the fact that the computational tasks in this situation are enormous. Therefore, it is necessary to select fast numerical methods; to develop parallel codes and, what is most important when the problems solved are very large to organize the computational process in a proper way.The last item (which is very often underestimated but, let us re-iterate, which is very important) is the major topic of this book. In fact, the proper organization of the computational process can be viewed as a preparation of templates which can be used with different numerical methods and different parallel devices. The development of such templates is described in the book. It is also demonstrated that many comprehensive environmental studies can successfully be carried out when the computations are correctly organized. Thus, this book will help the reader to understand better that, while (a) it is very important to select fast numerical methods as well as (b) it is very important to develop parallel codes, this will not be sufficient when the problems solved are really very large. In the latter case, it is also crucial to exploit better the computer architecture by organizing properly the computational process. - Use of templates in connection with the treatment of very large models - Performance of comprehensive environmental studies - Obtaining reliable and robust information about pollution levels - Studying the impact of future climatic changes on high pollution levels - Investigating trends related to critical levels of pollution

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392

Publisher

Elsevier

Published Date

ISBN 10

0080462480

ISBN 13

9780080462486

Computational Methods for General Sparse Matrices

By: Zahari Zlatev

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Computational Methods for General Sparse Matrices

By: Zahari Zlatev

Et moi ... - si j'avait su comment en revenir, One service mathematics has rendered the je n 'y serais point aile.' human race. It has put common sense back where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell 0. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'elre of this series.

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343

Publisher

Springer Science & Business Media

Published Date

ISBN 10

940171116X

ISBN 13

9789401711166

Computational and Numerical Challenges in Environmental Modelling

By: Zahari Zlatev,Ivan Dimov

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Computational and Numerical Challenges in Environmental Modelling

By: Zahari Zlatev,Ivan Dimov

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Page Count

392

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Elsevier

Published Date

ISBN 10

0080462480

ISBN 13

9780080462486

Computer Treatment of Large Air Pollution Models

By: Zahari Zlatev

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Computer Treatment of Large Air Pollution Models

By: Zahari Zlatev

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367

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Springer Science & Business Media

Published Date

ISBN 10

9401103119

ISBN 13

9789401103114

Advanced Numerical Methods for Complex Environmental Models: Needs and Availability

By: István Faragó,Ágnes Havasi,Zahari Zlatev

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Advanced Numerical Methods for Complex Environmental Models: Needs and Availability

By: István Faragó,Ágnes Havasi,Zahari Zlatev

High air pollution levels pose a significant threat to plants, animals and human beings. Efforts by researchers are directed towards keeping air pollution levels below well defined ‘critical‘ levels in order to maintain a sustainable atmosphere and environmental system. The application of advanced mathematical models is important for researchers to achieve this goal as efficiently as possible. Mathematical models can be used to predict answers to many important questions about the environment. This application comes with several complex theoretical and practical obstacles which need to be resolved. A successfully applicable mathematical model needs to enable researchers to • Mathematically describe all important physical and chemical processes. • Apply fast and sufficiently accurate numerical methods. • Ensure that the model runs efficiently on modern high speed computers. • Use high quality input data, both meteorological data and emission inventories, in the runs. • Verify the model results by comparing them with reliable measurements taken in different parts of the spatial domain of the model. • Carry out long series of sensitivity experiments to check the response of the model to changes of different key parameters. • Visualize and animate the output results in order to make them easily understandable even to non-specialists. This monograph thoroughly describes mathematical methods useful for various situations in environmental modeling - including finite difference methods, splitting methods, parallel computation, etc. - and provides a framework for resolving problems posed in relation to the points listed above. Chapters are written by well-known specialists making this book a handy reference for researchers, university teachers and students working and studying in the areas of air pollution, meteorology, applied mathematics and computer science.

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Page Count

437

Publisher

Bentham Science Publishers

Published Date

ISBN 10

160805778X

ISBN 13

9781608057788

Richardson Extrapolation

Practical Aspects and Applications

By: Zahari Zlatev,Ivan Dimov,István Faragó,Ágnes Havasi

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Richardson Extrapolation

Practical Aspects and Applications

By: Zahari Zlatev,Ivan Dimov,István Faragó,Ágnes Havasi

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343

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110531984

ISBN 13

9783110531985

Computational Methods for General Sparse Matrices

By: Zahari Zlatev

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Computational Methods for General Sparse Matrices

By: Zahari Zlatev

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Solve jigsaw puzzle

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343

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Springer Science & Business Media

Published Date

ISBN 10

940171116X

ISBN 13

9789401711166

Book's by Zahari Zlatev

Richardson Extrapolation

Richardson Extrapolation

Computer Treatment of Large Air Pollution Models

Computer Treatment of Large Air Pollution Models

Computational and Numerical Challenges in Environmental Modelling

Computational and Numerical Challenges in Environmental Modelling

Computational Methods for General Sparse Matrices

Computational Methods for General Sparse Matrices

Computational and Numerical Challenges in Environmental Modelling

Computational and Numerical Challenges in Environmental Modelling

Computer Treatment of Large Air Pollution Models

Computer Treatment of Large Air Pollution Models

Advanced Numerical Methods for Complex Environmental Models: Needs and Availability

Advanced Numerical Methods for Complex Environmental Models: Needs and Availability

Richardson Extrapolation

Richardson Extrapolation

Computational Methods for General Sparse Matrices

Computational Methods for General Sparse Matrices

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